# Properties

 Label 100.2.e Level $100$ Weight $2$ Character orbit 100.e Rep. character $\chi_{100}(7,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $14$ Newform subspaces $4$ Sturm bound $30$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$100 = 2^{2} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 100.e (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$20$$ Character field: $$\Q(i)$$ Newform subspaces: $$4$$ Sturm bound: $$30$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(100, [\chi])$$.

Total New Old
Modular forms 42 22 20
Cusp forms 18 14 4
Eisenstein series 24 8 16

## Trace form

 $$14 q + 2 q^{2} - 12 q^{6} - 4 q^{8} + O(q^{10})$$ $$14 q + 2 q^{2} - 12 q^{6} - 4 q^{8} + 2 q^{13} + 4 q^{16} - 6 q^{17} + 6 q^{18} - 24 q^{21} - 20 q^{26} - 8 q^{32} + 12 q^{36} + 14 q^{37} + 8 q^{41} + 48 q^{46} + 4 q^{52} - 18 q^{53} + 48 q^{56} - 8 q^{58} - 72 q^{61} + 60 q^{66} + 12 q^{68} + 12 q^{72} + 22 q^{73} - 60 q^{76} + 90 q^{81} - 16 q^{82} - 72 q^{86} - 132 q^{96} - 26 q^{97} - 14 q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(100, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
100.2.e.a $2$ $0.799$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-5})$$ $$-2$$ $$-2$$ $$0$$ $$6$$ $$q+(-1+i)q^{2}+(-1-i)q^{3}-2iq^{4}+\cdots$$
100.2.e.b $2$ $0.799$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ $$2$$ $$0$$ $$0$$ $$0$$ $$q+(1+i)q^{2}+2iq^{4}+(-2+2i)q^{8}+\cdots$$
100.2.e.c $2$ $0.799$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-5})$$ $$2$$ $$2$$ $$0$$ $$-6$$ $$q+(1-i)q^{2}+(1+i)q^{3}-2iq^{4}+2q^{6}+\cdots$$
100.2.e.d $8$ $0.799$ 8.0.3317760000.5 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(-\beta _{4}+\beta _{6})q^{3}+\beta _{2}q^{4}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(100, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(100, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(20, [\chi])$$$$^{\oplus 2}$$